# Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque

@article{Bartuccelli2017PeriodicAQ, title={Periodic and quasi-periodic attractors for the spin-orbit evolution of Mercury with a realistic tidal torque}, author={Michele V. Bartuccelli and Jonathan H. B. Deane and Guido Gentile}, journal={Monthly Notices of the Royal Astronomical Society}, year={2017}, volume={469}, pages={127-150} }

In this paper, we make a detailed study of the spin-orbit dynamics of Mercury, as predicted by the realistic model which has been recently introduced in a series of papers mainly by Efroimsky and Makarov. We present numerical and analytical results concerning the nature of the librations of Mercury’s spin in the 3:2 resonance. The results provide evidence that the librations are quasi-periodic in time, consisting of a slow oscillation, with an amplitude of order of arcminutes, superimposed on…

## 6 Citations

### Spin-orbital Tidal Dynamics and Tidal Heating in the TRAPPIST-1 Multiplanet System

- Physics, Geology
- 2018

We perform numerical simulations of the TRAPPIST-1 system of seven exoplanets orbiting a nearby M dwarf, starting with a previously suggested stable configuration. The long-term stability of this…

### Fast numerics for the spin orbit equation with realistic tidal dissipation and constant eccentricity

- Physics
- 2017

We present an algorithm for the rapid numerical integration of a time-periodic ODE with a small dissipation term that is $$C^1$$C1 in the velocity. Such an ODE arises as a model of spin–orbit…

### Rotation and figure evolution in the creep tide theory: a new approach and application to Mercury

- PhysicsCelestial Mechanics and Dynamical Astronomy
- 2019

This paper deals with the rotation and figure evolution of a planet near the 3/2 spin–orbit resonance and the exploration of a new formulation of the creep tide theory (Folonier et al. in Celest Mech…

### Pseudo-synchronous solutions for dissipative non-autonomous systems

- Mathematics, Physics
- 2021

In the framework of KAM theory, the persistence of invariant tori in quasi-integrable systems is proved by assuming a non-resonance condition on the frequencies, such as the standard Diophantine…

### Rotation of a synchronous viscoelastic shell

- Geology
- 2018

Several natural satellites of the giant planets have shown evidence of a global internal ocean, coated by a thin, icy crust. This crust is probably viscoelastic, which would alter its rotational…

### Triaxial deformation and asynchronous rotation of rocky planets in the habitable zone of low-mass stars

- Geology, Physics
- 2017

Rocky planets orbiting M-dwarf stars in the habitable zone tend to be driven to synchronous rotation by tidal dissipation, potentially causing difficulties for maintaining a habitable climate on the…

## References

SHOWING 1-10 OF 57 REFERENCES

### CONDITIONS OF PASSAGE AND ENTRAPMENT OF TERRESTRIAL PLANETS IN SPIN-ORBIT RESONANCES

- Physics, Geology
- 2012

The dynamical evolution of terrestrial planets resembling Mercury in the vicinity of spin-orbit resonances is investigated using comprehensive harmonic expansions of the tidal torque taking into…

### Mercury's capture into the 3/2 spin-orbit resonance as a result of its chaotic dynamics

- Physics, GeologyNature
- 2004

It is shown that the chaotic evolution of Mercury's orbit can drive its eccentricity beyond 0.325 during the planet's history, which very efficiently leads to its capture into the 3/2 resonance.

### The theory of secondary resonances in the spin–orbit problem

- Physics
- 2016

We study the resonant dynamics in a simple one degree of freedom, time dependent Hamiltonian model describing spin-orbit interactions. The equations of motion admit periodic solutions associated with…

### DYNAMICAL EVOLUTION AND SPIN-ORBIT RESONANCES OF POTENTIALLY HABITABLE EXOPLANETS. THE CASE OF GJ 667C

- Physics, Geology
- 2012

We investigate the spin-orbital evolution of the potentially habitable super-Earth GJ 667Cc in the multiple system of at least two exoplanets orbiting a nearby M dwarf. The published radial…

### Tidal synchronization of close-in satellites and exoplanets. III. Tidal dissipation revisited and application to Enceladus

- PhysicsCelestial Mechanics and Dynamical Astronomy
- 2018

This paper deals with a new formulation of the creep tide theory (Ferraz-Mello in Celest Mech Dyn Astron 116:109, 2013—Paper I) and with the tidal dissipation predicted by the theory in the case of…

### The high-order Euler method and the spin–orbit model.

- Computer Science
- 2014

An algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation, is presented and implemented in standard double precision arithmetic.

### Tidal synchronization of close-in satellites and exoplanets: II. Spin dynamics and extension to Mercury and exoplanet host stars

- Physics, Geology
- 2015

This paper deals with the application of the creep tide theory (Ferraz-Mello, Celest Mech Dyn Astron 116:109, 2013a) to the rotation of close-in satellites, Mercury, close-in exoplanets, and their…